theorem Th123:
  for n st n > 1 holds ((a,b) followed_by c).n = c
proof
  let n;
  assume
A1: n > 1;
  dom (0,1) --> (a,b) = {0,1} by FUNCT_4:62;
  then
A2: not n in dom (0,1) --> (a,b) by A1,TARSKI:def 2;
A3: n in NAT by ORDINAL1:def 12;
  thus ((a,b) followed_by c).n = ((NAT --> c) +* ((0,1) --> (a,b))).n
    .= (NAT --> c).n by A2,FUNCT_4:11
    .= c by A3,FUNCOP_1:7;
end;
